Aeronautical industries are concerned about generating efficient and cost-effective statistical design allowables of composite laminate responses. Within this framework of uncertainty quantification and management (UQ & M), accounting for the various uncertainties is crucial to calculate the design allowables which, in turn, adds confidence to the design and certification process. In this context, as a precursor to UQ & M, we establish a global sensitivity analysis framework to identify the material properties that influence the laminate responses. In this study, an open hole tensile (OHT) test configuration is considered. In a first step, sensitivity analysis based on an analytical model is performed using Sobol, FAST, and Morris methods, whereas in a second step, sensitivity analysis based on a detailed 3D finite element model (FEM) incorporating damage is performed using Morris. The paper compares different sensitivity approaches in terms of computational cost and results. Further, different case studies (varied notched hole sizes, width-to-diameter ratios, laminate stacking sequences, etc.) are performed to study how the sensitive parameters vary for different configurations. The study identified the Morris method, along with the selected hyper parameters, as being suitable for FEM based sensitivity analysis due to its low computational cost. Five material properties (out of 23) were identified as influencing the open hole laminate tensile strength. Using the FE simulations performed for the Morris analysis, a first estimation of the design allowables (A and B basis values) on the OHT strength is also presented. The results from this paper contribute to the next step of UQ&M, where only the identified sensitive material properties can be considered for detailed experimental characterization or for building meta models to calculate the design allowables. A framework like this, complements experimental campaign to reduce the associated costs and knock-down factors, thus shortening the certification process.